Numerous extensions to the proposed approach can be considered. One argument for simulation-based design is the ease with which sensitivity to model assumptions, such as the value of nuisance parameters, can be assessed [1]}. Future work could consider how a systematic assessment of sensitivity to nuisance parameters could be conducted, given a proposed trial design. Such investigations fall under the heading of uncertainty quantification and can be carried out using GP regression and associated techniques [2]}. A further extension could consider Bayesian approaches to trial design, including hybrid Bayesian-frequentist assurances [3]}, fully Bayesian measures such as average coverage criterion [4]}, and decision-theoretic methods [5]}. Aside from very simple cases involving only conjugate analyses, evaluating these Bayesian criteria will generally require simulation [3]} and so optimal design may benefit from the efficient methods discussed here. Complex SSD problems are also common in the area of adaptive designs, which can aim to minimise the expected sample size under several different hypotheses and over a number of stopping rule parameters [7]}. Extending the proposed methods to such problems would require using surrogate models to approximate the objective functions, as opposed to only the constraints.
